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Zbl 1214.34059
Baštinec, J.; Dibl{\'\i}k, J.; Khusainov, D.Ya.; Ryvolová, A.
Exponential stability and estimation of solutions of linear differential systems of neutral type with constant coefficients. (English)
[J] Bound. Value Probl. 2010, Article ID 956121, 20 p. (2010). ISSN 1687-2770/e

The paper deals with the linear systems of neutral differential equations with constant coefficients and a constant delay of the form $$\dot{x}(t)=D\dot{x}(t-\tau)+Ax(t)+Bx(t-\tau),$$ where $t\geq 0$, $\tau>0$, $A,B,$ and $D$ are $n\times n$ constant matrices, and $x:[-\tau,\infty)\to\Bbb{R}^n$ is a column vector-solution. The authors investigate the exponential-type stability of such systems using Lyapunov-Krasovskii type functionals. Delay-dependent conditions sufficient for the stability are formulated in terms of positivity of auxiliary matrices. Illustrative examples are shown and comparisons with known results are given.
[Jan Ohriska (Košice)]

MSC 2000:: *34K20 Stability theory of functional-differential equations
34K40 Neutral equations
34K06 Linear functional-differential equations

Keywords: stability theory; neutral equations; linear functional-differential equations

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Zentralblatt MATH Berlin [Germany]